As part of my story, a letter is sent from England to America in 1890. I was wondering if there was a way to work out how long it would take and perhaps the cost of writing and sending letters.
It took about two weeks. By 1890 postal unions had been formed allowing mail to transit around the world to most places. The domestic rate in the US was 2¢ per ounce. For a first class letter weighing 1/2 ounce or less to Britain the union cost would be an additional 5¢. Thus, the total cost was 7¢ for a first class letter.
Here are the rates from 1890, excerpted to show Great Britain:
In 1890, in Massachusetts a skilled laborer received between $15 and $20 for a 60-hour work week, or between 25¢ and 33¢ an hour.
A rough estimate of the time is as follows: the distance from London to NY is approximately 3000 (nautical) miles. The Blue Riband prize was awarded to passenger liners which showed the average speed of about 15 knots, (20 knots was the world record in 1889), so I suppose it is safe to assume that an average ship at that time could cross with the average speed of 10 knots. This makes 300 hours = 12 days. This is the crossing only, and if you send your letter from London to NY.
With this estimate one could probably hope that from SOME place in Europe to SOME place in the US it may take from 3 weeks to a month.
(Nowadays when the mail is transported by airplanes it can still easily take more than a month, sometimes much more, for a letter or a small package to reach from Germany to US Midwest: personal experience).
The question about the price is probably ill defined. I suppose some fast delivery options were available for extra price like they are available nowadays.
My general impression is that there was no big progress in the speed of the (cheapest) mail from 1890 to the present.
EDIT. Here is a web page with some 19 century stamped envelopes, showing dates sent and received; the price of a British stamp is easily fund on the Internet: